Mixed Membership Models for Multilevel Functional Data

TL;DR

This paper introduces a hierarchical mixed membership model for multilevel functional data, enabling partial class memberships and scalable analysis, demonstrated on EEG data from children with ASD.

Contribution

It extends mixed membership models to multilevel functional data using a hierarchical Karhunen-Loeve approach with a novel prior for identifiability.

Findings

Model effectively captures partial memberships in EEG data.

Hierarchical approach improves scalability and flexibility.

Application to autism EEG data demonstrates practical utility.

Abstract

Mixed membership models extend classical clustering by substituting the notion of uncertain membership with the notion of mixed membership. In particular, these models allow each observation to partially belong to multiple pure membership classes. We discuss mixed membership models for functional data by extending the framework to multilevel functional observations. We show how the classical multivariate Karhunen-Loeve decomposition can be translated into a simple hierarchical model for scalable and flexible expressivity of the underlying stochastic processes. The identifiability of partial membership structures is aided by the definition of a hierarchical repulsive prior on the unitary simplex. Our work is motivated and illustrated by applications to a study on functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD).